How to do an action when a checkbox is checked with jQuery?

What you are looking for is called an Event. JQuery provides simple event binding methods like so

$("#home").click(function() {
    // this function will get executed every time the #home element is clicked (or tab-spacebar changed)
    if($(this).is(":checked")) // "this" refers to the element that fired the event
    {
        alert('home is checked');
    }
});

you need to use the .click event described here: http://docs.jquery.com/Events/click#fn

so

$("#home").click( function () {
    if($("#home").is(":checked"))
    {
      alert('');
    }
});

Actually the change() function is much better for this solution because it works for javascript generated actions, such as selecting every checkbox via a script.

$('#home').change(function() {
   if ($(this).is(':checked')) {
      ... 
   } else {
      ...
   }
});